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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase distributions of a two-mode squeezed coherent state

A. Lukš, Vlasta Peřinová

Published Jan 1, 1998• 0 citations
Publisher

Abstract

In experiments, pulses of two-mode squeezed light were generated by an optical parametric amplifier. For certain ranges of parameters the joint photon number distribution of two-mode squeezed coherent states exhibits nonclassical oscillations. The nonclassical features were explained using the interference-in-phase-space concept in four-dimensional phase space. We investigate joint phase distribution of two- mode squeezed coherent states for presence of peaks and attempt to relate the peaks to the manifest oscillations in the joint photon number distribution.

DOI
10.1117/12.301357

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In experiments, pulses of two-mode squeezed light were generated by an optical parametric amplifier. For certain ranges of parameters the joint photon number distribution of two-mode squeezed coherent states exhibits nonclassical oscillations. The nonclassical features were explained using the interference-in-phase-space concept in four-dimensional phase space. We investigate joint phase distribution of two- mode squeezed coherent states for presence of peaks and attempt to relate the peaks to the manifest oscillations in the joint photon number distribution.
We derive the joint photon-number distribution for two-mode squeezed states with coherent amplitudes. For certain ranges of the parameters, the joint distribution exhibits nonclassical oscillations, which are the two-mode analog of the oscillations found in the single-mode case. These nonclassical oscillations are absent from the marginal distributions for each mode. The nonclassical features of the joint distribution may be explained using the interference--in--phase-space concept in four-dimensional phase space.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.
Two-mode squeezed coherent states with complex squeeze and displacement parameters are studied, taking advantage of the SU(2) dynamical symmetry underlying two-mode systems. Expressions for the photon distributions in such states are derived using an SU(2) identity and the fact that the two-mode squeeze operator can be viewed as a rotated version of the product of reciprocal single-mode squeeze operators. An important U(1)\ifmmode\times\else\texttimes\fi{}U(1) invariance of this photon distribution is established. As a consequence, the three phases of the complex squeeze and displacement parameters enter the photon distribution through just one U(1)\ifmmode\times\else\texttimes\fi{}U(1) invariant combination. An associated Gouy effect is noted. Numerical examples of two-mode photon distributions are shown, and interesting new features demonstrated. Second-order coherence properties and their nonclassical nature are briefly studied.
The properties of correlated two-mode SU(1, 1) coherent states are studied. These states are a generalization of the two-mode squeezed vacuum states and are generated by applying the two-mode squeeze operator to a state in which there are initially q photons in one mode, |q, 0〉, the squeezed vacuum (q = 0) obviously being a special case. For these states the photon-number distribution and the nonclassical properties of photon antibunching, enhanced phase fluctuations, violations of the Cauchy–Schwarz inequality, two-mode squeezing, and sum squeezing are studied. A Q-function quasi-probability distribution for these states is also presented.
We present a versatile method for producing two-mode stabilized squeezed coherent state (SSCS) of light with controllable nonclassicality. Our method involves seeding phase-coherent bichromatic fields into a nondegenerate optical parametric oscillator (OPO), where the global phase difference Φ\PhiΦ between the bichromatic seed and pump fields plays a central role. When Φ=2nπ\Phi=2n\piΦ=2nπ, where nnn is an integer, we show that the two-mode SSCS has its nonclassical measure at its minimum possible value with an effective displacement that compensates for single-photon losses with injected photons. As a result, the SSCS has a larger mean photon number and controllable nonclassicality compared to an OPO without seed fields. We also show that near-perfect squeezing level can be obtained at that effective displacement without being subject to injection rates. We believe that the proposed quantum source of two-mode SSCS with controllable nonclassicality would be useful for continuous-variable photonic quantum information processing.